Beispielaufgaben Algebra - Grundlagen - Potenzen

Algebra-Grundlagen-Potenzen

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Beispiel Nr: 16

\begin{array}{l} a^{m} \cdot a^{n} = a^{m + n} \\ \frac{a^{m}}{a^{n}} = a^{m - n} \\ a^{n} \cdot b^{n} = (a b)^{n} \\ (a^{n})^{m} = a^{n \cdot m} \\ Gegeben: \\ a = - \frac{1}{2} b = 3 m = 2 n = 3 \\ Rechnung: \\ {(- \frac{1}{2})}^{2} \cdot {(- \frac{1}{2})}^{3} = {(- \frac{1}{2})}^{2 + 3} = {(- \frac{1}{2})}^{5} = - \frac{1}{32} \\ {(- \frac{1}{2})}^{2} : {(- \frac{1}{2})}^{3} = \frac{{(- \frac{1}{2})}^{2}}{{(- \frac{1}{2})}^{3}} = {(- \frac{1}{2})}^{2 - 3} = {(- \frac{1}{2})}^{- 1} = - 2 \\ {(- \frac{1}{2})}^{3} \cdot 3^{3} = ((- \frac{1}{2}) \cdot 3)^{3} = {(- 1 \frac{1}{2})}^{3} = - 3 \frac{3}{8} \\ ({(- \frac{1}{2})}^{3})^{2} = {(- \frac{1}{2})}^{3 \cdot 2} = {(- \frac{1}{2})}^{6} = \frac{1}{64} \end{array}